Oddly enough, not that much. You'll have a lot of emotion, and lots of ink spilled, but little will change for the day to day life of most people: They have their lives to worry about, aliens are cool, but don't put bread on the table.
Governments will race to get a mission with humans to visit.
What happens next depends on if there are living aliens there, or just an old city.
Maybe not on our daily lives, so I don't think (I hope..) there will not be wide spread panic. Maybe a few groups here and there but nothing we've never seen before.
What I would expect though, and I consider this a big deal, is the potential for humans to start answering one of life's most intriguing questions: are we, or are we not alone in this Universe? Like Clarke famously said, both alternatives are pretty scary.
So at least I would hope people would start pressuring governments to actually go there and make contact. As a lot of other people say, humans seem to be explorers by nature.
However there's the other fact that someone else posted. Probably this would not be know at first, so it's harder to gauge with that factor. I don't think NASA/Gov would release this info right away, but I do think if this info is ever released, it would make the world change a lot. Maybe not immediately, but for sure on the mid-to-long term.
But, when that mission arrives to inspect the lights, couldn't we expect that contact with alien technology, even if it is just an alien laser, to profoundly change our science?
If you went back in time and gave Isaac Newton a smartphone but didn't tell him what it was, how it worked or even charged the batteries, it probably wouldn't change much of anything for a very long time. And that would possibly be a lot less alien in context than any actual alien technology we come across.
But let's assume it does. Our science has changed profoundly many times.
For example: Heliocentric solar system, Nuclear Bomb, and radio, just to give some of the most dramatic changes.
Did all that much change on Earth? Most people just went on like normal. Things changed, but slowly, there was no shock.
Can you imagine someone from long ago, who is told "We just found a way to speak to someone 300 miles away in an instant." They would probably go nuts imagining the immense change in peoples lives, in war, in commerce.
Yet, these changes actually happened, and while things changed, there was no turmoil.
The reality was not as dramatic as the expectation.
Before technology most people lived on farms. Hardly anyone travelled more than a few tens of miles at most. Infant mortality was huge. Adult mortality was almost as huge. Living to fifty made you exceptional.
The average person had no education to speak of - no math, no ability to read or write, no knowledge of science, art, or culture.
The single biggest change is the fact that not only can most people read and write, but they have a vastly increased awareness of the world around them.
Now - imagine if that awareness was increased again to the interplanetary or galactic level. Imagine if live expectancy increased by a factor of two, or five, or ten. Imagine having access to a galaxy-sized Internet, with its own version of Wikipedia (and whatever the alien equivalent of Hacker News is).
No big changes? I really doubt that.
"Grand Contested Election for the Presidency of the United States. "WHALING VOYAGE BY ONE ISHMAEL. "BLOODY BATTLE IN AFFGHANISTAN."
Published 1851. The more things change, the more things stay the same.